Abstract: The genus distribution of a graph G is defined to be the sequence {g_k}, where g_k is the number of different embeddings of G in the closed orientable surface of genus k. In this paper, a recurrence formula of the genus distribution for a standard circle-like graph is obtained,and a computing formula of the embedding for a circle-ike graph is given.

Key words: Circle-like graph, Embedding, Orientable surface, Embedding polynomial